Determination of the number of psi(3686) events at BESIII

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Determination of the number of ψ(3686) events at BESIII

To cite this article: M. Ablikim et al 2018 Chinese Phys. C 42 023001

Determination of the number of ψ(3686) events at BESIII

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Received 13 September 2017, Revised 2 December 2017, Published online 5 January 2018

∗ Supported by the Ministry of Science and Technology of China (2009CB825200), National Natural Science Foundation of China (NSFC) (11235011, 11322544, 11335008, 11425524, 11475207), the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program, the Collaborative Innovation Center for Particles and Interactions (CICPI), Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (11179014), Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (11179007, U1232201, U1532257, U1532258), Joint Funds of the National Natural Science Foundation of China (11079008), CAS (KJCX2-YW-N29, KJCX2-YW-N45), 100 Talents Program of CAS, National 1000 Talents Program of China, German Research Foundation DFG (Collaborative Research Center CRC 1044), Istituto Nazionale di Fisica Nucleare, Italy, Koninklijke Nederlandse Akademie van Wetenschappen (KNAW) (530-4CDP03), Ministry of Development of Turkey (DPT2006K-120470), National Natural Science Foundation of China (11205082), The Swedish Research Council, U. S. Department of Energy (DE-FG02-05ER41374, DE-SC-0010118, DE-SC-0010504), U.S. National Science Foundation, University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt, WCU Program of National Research Foundation of Korea (R32-2008-000-10155-0)

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3_{and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy}

E. H. Thorndike41 _{D. Toth}40 _{I. Uman}37D _{G. S. Varner}39 _{B. Wang(R)}28 _{D. Wang(À)}29 _{D. Y. Wang(Œ}

])29 _{K. Wang(‰)}1 _{L. L. Wang( )}1 _{L. S. Wang((Ô)}1 _{M. Wang(ƒ)}31_{P. Wang(²)}1 _{P. L. Wang(}

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Z. Y. Zhang(܉)47_{G. Zhao(ë1)}1_{J. W. Zhao(뮕)}1 _{J. Z. Zhao(ë®±)}1 _{Lei Zhao(ëX)}42_{Ling Zhao(ë )}1

M. G. Zhao(ë²f)28_{Q. Zhao(ër)}1_{Q. W. Zhao(ëŸ!)}1 _{S. J. Zhao(ëÖd)}49_{T. C. Zhao(ëU³)}1_{Y. B. Zhao(ë}

þR)1 _{Z. G. Zhao(ëI)}42 _{A. Zhemchugov}21,a _{B. Zheng(xÅ)}43 _{J. P. Zheng(xï²)}1 _{Y. H. Zheng(xð)}38

B. Zhong(¨Q)26_{L. Zhou(±s)}1 _{X. Zhou(±)}47 _{X. K. Zhou(±¡x)}38_{X. R. Zhou(±I)}42_{X. Y. Zhou(±,Œ)}1

K. Zhu(Áp)1 _{K. J. Zhu(Á‰
)}1 _{X. L. Zhu(ÁƒX)}36_{Y. C. Zhu(ÁCS)}42 _{Y. S. Zhu(Á[))}1,38 _{Z. A. Zhu(Ág}

S)1,38 _{J. Zhuang(Bï)}1 _{B. S. Zou(qXt)}1 _{J. H. Zou(qZð)}1

(BESIII Collaboration)

1_{Institute of High Energy Physics, Beijing 100049, China} 2 _{Beihang University, Beijing 100191, China}

3_{Beijing Institute of Petrochemical Technology, Beijing 102617, China} 4_{Bochum Ruhr-University, D-44780 Bochum, Germany} 5_{Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA}

6 _{Central China Normal University, Wuhan 430079, China} 7_{China Center of Advanced Science and Technology, Beijing 100190, China}

8 _{COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan} 9 _{G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia}

10_{GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany} 11_{Guangxi Normal University, Guilin 541004, China}

12_{Guangxi University, Nanning 530004, China} 13_{Hangzhou Normal University, Hangzhou 310036, China}

14_{Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany} 15_{Henan Normal University, Xinxiang 453007, China}

16_{Henan University of Science and Technology, Luoyang 471003, China} 17_{Huangshan College, Huangshan 245000, China}

18_{Hunan University, Changsha 410082, China} 19 _{Indiana University, Bloomington, Indiana 47405, USA}

20_{(A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN and University of Perugia, I-06100, Perugia, Italy} 21_{(A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy}

22_{Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany} 23_{Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia}

24_{Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany} 25_{KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands}

26_{Lanzhou University, Lanzhou 730000, China} 27_{Liaoning University, Shenyang 110036, China} 28_{Nanjing Normal University, Nanjing 210023, China}

29_{Nanjing University, Nanjing 210093, China} 30_{Nankai University, Tianjin 300071, China} 31_{Peking University, Beijing 100871, China} 32_{Seoul National University, Seoul, 151-747 Korea}

33_{Shandong University, Jinan 250100, China} 34_{Shanghai Jiao Tong University, Shanghai 200240, China}

35_{Shanxi University, Taiyuan 030006, China} 36_{Sichuan University, Chengdu 610064, China}

37_{Soochow University, Suzhou 215006, China} 38_{Sun Yat-Sen University, Guangzhou 510275, China}

39_{Tsinghua University, Beijing 100084, China}

40_{(A)Ankara University, 06100 Tandogan, Ankara, Turkey; (B)Istanbul Bilgi University, 34060 Eyup, Istanbul, Turkey; (C)Uludag}

University, 16059 Bursa, Turkey; (D)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey

42 _{University of Hawaii, Honolulu, Hawaii 96822, USA} 43_{University of Minnesota, Minneapolis, Minnesota 55455, USA}

44_{University of Rochester, Rochester, New York 14627, USA} 45_{University of Science and Technology Liaoning, Anshan 114051, China}

46_{University of Science and Technology of China, Hefei 230026, China} 47_{University of South China, Hengyang 421001, China}

48_{University of the Punjab, Lahore-54590, Pakistan}

49_{(A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125,}

Turin, Italy

50_{Uppsala University, Box 516, SE-75120 Uppsala, Sweden} 51_{Wuhan University, Wuhan 430072, China} 52_{Zhejiang University, Hangzhou 310027, China} 53_{Zhengzhou University, Zhengzhou 450001, China}

a_{Also at State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, China} b_{Also at Bogazici University, 34342 Istanbul, Turkey}

c_{Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia} d_{Also at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia}

e _{Also at the Novosibirsk State University, Novosibirsk, 630090, Russia} f _{Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russia}

g _{Also at University of Texas at Dallas, Richardson, Texas 75083, USA} h_{Also at Istanbul Arel University, 34295 Istanbul, Turkey} i_{Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany}

Abstract: The numbers of ψ(3686) events accumulated by the BESIII detector for the data taken during 2009 and

2012 are determined to be (107.0±0.8)×106 and (341.1±2.1)×106, respectively, by counting inclusive hadronic events,

where the uncertainties are systematic and the statistical uncertainties are negligible. The number of events for the sample taken in 2009 is consistent with that of the previous measurement. The total number of ψ(3686) events for

the two data taking periods is (448.1±2.9)×106.

Keywords: ψ(3686), inclusive process, hadronic events, Bhabha process

PACS: 13.25.Gv, 13.66.Bc, 13.20.Gd DOI:10.1088/1674-1137/42/2/023001

1

Introduction

During two data taking periods, one in 2009 and one in 2012, the BESIII experiment accumulated the world’s largest ψ(3686) data sample produced in electron-positron collisions, which provides an excellent resource to precisely study ψ(3686) transitions and decays and those of daughter charmonium states, e.g. χcJ,hc, and

ηc, as well as to search for rare decays for physics beyond

the standard model. The number of ψ(3686) events,

Nψ(3686), is a crucial parameter, and its precision will

directly affect the accuracy of these measurements. In this paper, we present the determination of

Nψ(3686) using inclusive ψ(3686) hadronic decays, whose

branching fraction is known rather precisely, (97.85 ± 0.13)% [1]. In the analysis, the QED background yield under the ψ(3686) peak is evaluated by analyzing the two sets of off-resonance data taken close in time with the peak samples, i.e. center-of-mass energy√s = 3.65 GeV collected in 2009 and four energy points ranging from 3.542 to 3.600 GeV collected in 2012 for a τ -mass scan. The strategy for the background estimation was success-fully used in our previous measurement of the number of ψ(3686) events collected in 2009 [2].

2

BESIII detector and Monte Carlo

sim-ulation

BEPCII is a double-ring e+_e− _{collider that has}

reached a peak luminosity of 1×1033 _cm−2_s−1 _at √_s=

3.773 GeV. The cylindrical core of the BESIII detector consists of a helium-based main drift chamber (MDC), a plastic scintillator time-of-flight (TOF) system, and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a superconducting solenoid magnet with a field strength of 1.0 T (0.9 T in 2012). The solenoid is supported by an octagonal flux-return yoke with resistive plate counter modules interleaved with steel as a muon identifier. The acceptance for charged particles and pho-tons is 93% over the 4π stereo angle. The charged-particle momentum resolution at 1 GeV/c is 0.5%, and the photon energy resolution at 1 GeV is 2.5% (5%) in the barrel (end-caps) of the EMC. More details about the apparatus can be found in Ref. [3]. The MDC encoun-tered the Malter effect [4] due to cathode aging during ψ(3686) data taking in 2012. This effect was suppressed by mixing about 0.2% water vapor into the MDC oper-ating gas [5] and can be well modeled by Monte Carlo (MC) simulation. The other sub-detectors worked well during 2009 and 2012.

The BESIII detector is modeled with a MC simula-tion based on geant4 [6]. The ψ(3686) produced in the electron-positron collisions are simulated with the gen-erator kkmc [7], which includes the beam energy spread according to the measurement of BEPCII and the ef-fect of initial state radiation (ISR). The known decay modes of ψ(3686) are generated with evtgen [8] ac-cording to the branching fractions in the Particle Data Group, PDG [1], while the remaining unknown decays are simulated using the lundcharm model [9]. The MC events are generated with mixing of randomly triggered events (non-physical events from collision) in data tak-ing to take into account the possible effects from beam-related backgrounds, cosmic rays, and electronic noise.

3

Event selection

The data collected at the ψ(3686) peak includes sev-eral different processes, i.e., ψ(3686) decays to hadrons or lepton pairs (e+_e−_{, µ}+_µ−_{, and τ}+_τ−_{), radiative return}

to the J/ψ, J/ψ decay due to the extended tail of the J/ψ line shape, and non-resonant (QED) processes, namely continuum background, including e+_e−_→γ∗_{→ hadrons,}

lepton pairs, and e+_e−_{→ e}+_e−_{+ X (X=hadrons,}

lep-ton pairs). The data also contains non-collision events, e.g. cosmic rays, beam-associated backgrounds, and elec-tronic noise. The process of interest in this analysis is ψ(3686) decaying into hadrons.

Event selection includes track and photon level se-lection and event level sese-lection. Charged tracks are re-quired to be within 1 cm of the beam line in the plane perpendicular to the beam and within ±10 cm from the Interaction Point (IP) in the beam direction. Showers reconstructed in the EMC barrel region (|cosθ| < 0.80) must have a minimum energy of 25 MeV, while those in the end-caps (0.86<|cosθ|<0.92) must have at least 50 MeV. The photons in the polar angle range between the barrel and end-caps are excluded due to the poor resolu-tion. A requirement of the EMC cluster timing [0, 700] ns is applied to suppress electronic noise and energy de-posits unrelated to the event.

At least one charged track is required for each can-didate event. In the following, the selected events are classified into three categories according to the multi-plicity of good charged tracks, i.e., Ngood= 1, Ngood= 2,

and Ngood>2, and named type-I, II, and III, respectively.

For type-III events, no further selection criteria are required. For type-II events, the momentum of each track is required to be less than 1.7 GeV/c and the opening angle (∆α) between the two charged tracks is

required to be less than 176◦ _{to suppress Bhabha and}

dimuon backgrounds. Figures 1 and 2 show the scatter plots of the momentum of the first charged track versus that of the second charged track, and the distribution of the opening angle between the two charged tracks for the

type-II candidates from simulated Bhabha (top) and in-clusive ψ(3686) (bottom) MC events, respectively. Fur-ther, an energy fraction requirement Evisible/Ecm>0.4 is

applied to suppress the low energy background (LEB), comprised mostly of e+_e−_{→ e}+_e−_{+X and double ISR}

events (e+_e−_{→ γ}

ISRγISRX). Here, Evisible is the visible

energy which is defined as the total energy of all charged tracks (calculated with the track momentum assuming the tracks to be pions) and neutral showers, and Ecm

is the center-of-mass energy. Figure 3 (top) shows the

Evisible/Ecm distributions of the type-II events for the

ψ(3686) data and inclusive MC sample. The visible ex-cess in data at low energy is from the LEB events. Un-less noted, in all plots, the points with error bars are the ψ(3686) data collected in 2012, and the histogram is the corresponding MC simulation.

(GeV/c)

P

(GeV/c)

P

(GeV/c)

P

(GeV/c)

P

Fig. 1. (color online) Scatter plots of the

momen-tum of the first charged track versus that of second charged track of type-II candidates for (top) Bhabha and (bottom) inclusive ψ(3686) MC events. In the bottom plot, the event accumula-tion in the top-right corner comes from ψ(3686)→

e+_e−_,µ+_µ−_{, while the different event bands}

nearby come from ψ(3686)→neutral+J/ψ,J/ψ→

e+_e−_,µ+_µ− _{etc. The event band in the}

bottom-left comes from ψ(3686) → π+π−_{J/ψ,J/ψ →}

e+_e−_,µ+_µ− _{with lepton pairs missing. The}

horizontal and vertical lines show the selection requirements to suppress Bhabha and dimuon events.

(degree)

∆

Events/0.2 degree

(degree)

∆

Events/0.2 degree

Fig. 2. (color online) Distributions of the opening

angle between the two charged tracks for the type-II candidates from (top) Bhabha and (bottom) inclusive ψ(3686) MC events after applying the momentum requirement for two tracks (P <1.7 GeV/c). The arrow shows the angle requirement used to suppress Bhabha and dimuon events.

For type-I events, at least two photons are required in an event. Compared to those events with high charged track multiplicity, the type-I sample has more background according to the vertex distribution of the charged tracks. Thus, a neutral hadron π0 _{candidate is}

required to suppress the background events [10], where the π0_{candidate is reconstructed by any γγ combination.}

In an event, only the π0 _{candidate with a mass closest}

to π0 _{nominal value and satisfying |M}

γγ−Mπ0| < 0.015

MeV/c2 _{is kept for further analysis. Figure 4 shows}

the Mγγ distribution of selected π0 candidates for

type-I events. With the above selection criteria, the cor-responding Evisible/Ecm distributions of the candidate

events for the ψ(3686) data and inclusive MC sample are shown in Fig. 3 (bottom). An additional requirement

Evisible/Ecm> 0.4 is used to suppress the LEB events.

To discriminate the non-collision background from the collision events, the average vertex position in the Z direction is defined: ¯ VZ= N_good P i=1 Vi Z Ngood , where Vi

Z is the (signed) distance along the beam

direc-tion between the point of closest approach of the ith_track

and the IP. The ¯VZdistributions of the accepted hadronic

events for the ψ(3686) and off-resonance data are shown in the top and bottom plots of Fig. 5, respectively. The events satisfying | ¯VZ|<4 cm are taken as signal, while the

events in the sideband region 6<| ¯VZ|<10 cm are taken

as non-collision background events. The number of the observed hadronic events (Nobs_{) is obtained by counting}

the events in the signal region (Nsignal) and

subtract-ing the non-collision background contribution estimated from the events in the sideband regions (Nsideband) [11].

Nobs_=N

signal−Nsideband. (1)

We also determine the number of hadronic events by fit-ting the ¯VZ distribution, where the signal event shape is

described with a double Gaussian function, and the non-collision background is described with a second-order polynomial function. The resultant fit curves are shown in Fig. 5. This approach is used as a cross check and to estimate the corresponding systematic uncertainty.

/E

E

Events/0.02

/E

E

Events/0.02

Fig. 3. (color online) Distribution of Evisible/Ecm

for the (top) type-II and (bottom) type-I events. The MC distributions are scaled to have the same

)

(GeV/c

M

Events/0.5 MeV

Fig. 4. (color online) Distribution of Mγγin the π0

mass region for the type-I events.

(cm)

V

Entries/0.05cm

(cm)

V

Entries/0.05cm

(cm)

V

Entries/0.05cm

(cm)

V

Entries/0.05cm

Fig. 5. (color online) Fits to the ¯VZdistributions of

the accepted hadronic events in the (top) ψ(3686) and (bottom) off-resonance data. The solid (red) and dashed (pink) curves show the double Gaus-sian line shapes for the signal and the dotted (blue) lines show the polynomial function for the non-collision events.

4

Background subtraction

In general, the observed number of QED events can be estimated by

NQED

=L·σ·, (2)

where L is the integrated luminosity, σ is the theoretical cross section for the QED processes, and  is the effi-ciency determined from a MC simulation. Alternatively, as mentioned in Section 1, the off-resonance data samples can be used to estimate the continuum QED background yield. We apply the same approach to determine the yields of collision events and their uncertainties for the off-resonance data samples, which are dominated from the continuum QED processes. With the above method, the effect of QED background is independent of the MC simulation and the corresponding systematic bias is ex-pected to be small.

For the ψ(3686) and off-resonance data samples, the backgrounds from the radiative return to the J/ψ and J/ψ decay due to the extended tail are very similar due to the small difference in the center-of-mass energies. The total cross sections for these two processes are estimated to be 1.11 nb and 1.03 nb at the ψ(3686) peak and the off-resonance energy point, respectively [12]. Detailed MC studies show that the efficiencies for the continuum processes are equal at these two energy points. There-fore, the off-resonance data can be employed to subtract both the continuum QED and J/ψ decay backgrounds using a scaling factor, f, determined from the integrated luminosity multiplied by a factor of 1

s to account for the

energy dependence of the cross section,

f = Lψ(3686)

Loff−resonance·

soff−resonance

sψ(3686)

, (3)

where Lψ(3686) and Loff−resonance are the integrated

lumi-nosities for the ψ(3686) and off-resonance data samples, respectively, and sψ(3686) and soff−resonance are the

cor-responding square of center-of-mass energies. For the τ -scan data, the average energy is determined to be √

s =3.572 GeV. The scaling factors f are determined to be 3.61 and 20.56 for the 2009 and 2012 data samples, respectively.

The integrated luminosities of the data samples taken at different energy points are determined from e+_e−_→γγ

events using the following selection criteria. Each event is required to have no good charged tracks and at least two showers. The energies for the two most energetic showers must be higher than 1.6 GeV, and the cosine of the polar angle of each electromagnetic shower must be within the region |cosθ| < 0.8. The two most energetic showers in the ψ(3686) rest frame must be back to back with azimuthal angles ||φ1−φ2|−180◦| < 0.8◦. The

lu-minosities are 161.63±0.13 pb−1

and 506.92±0.23 pb−1

for ψ(3686) data taken during 2009 and 2012, respec-tively, while 43.88±0.07 pb−1

and 23.14±0.05 pb−1 _for

off-resonance data taken at √s=3.65 GeV and for the τ -scan data set [13], respectively. Here, the errors are statistical only. The systematic uncertainties related to the luminosity almost cancel in calculating the scaling

factor due to the small difference between the energy points.

/E

E

Events/0.005

/E

E

Events/0.005

Fig. 6. (color online) Comparison of the Evisible/

Ecm distributions for the (top) type-I and

(bot-tom) type-II LEB events between the ψ(3686) and scaled off-resonance data. The dots with error bars are the former, and the shaded histogram is the latter.

In order to show that the shape of the LEB events in off-resonance data is consistent with that in the ψ(3686)

sample, and, therefore, scaled off-resonance data can be used to remove LEB background in the ψ(3686) sample, we select an LEB sample by requiring Evisible/Ecm<0.35,

where few QED events are expected. Figure 6 (top and bottom) shows the comparisons of the Evisible/Ecm

dis-tributions for the type-I (top) and type-II (bottom) LEB events between the ψ(3686) and the scaled off-resonance data samples taken in 2012. The ratios of the number of events between the ψ(3686) peak and the off-resonance energy are 22.78 and 22.57 for the type I and type II events, respectively. Compared with the scaling factor obtained from the integrated luminosity normalization in Eq. (3), a difference of 10% is found for the type-I and type-II events. Similar differences are found for the 2009 data sample [2]. Since the fraction of LEB events in the selected sample is very small, the effect of this difference for the background estimation is negligible.

The cross sections for e+_e−_{→ τ}+_τ− _{are 0.67, 1.84,}

and 2.14 nb at the τ -scan energy (√s=3.572GeV accord-ing to luminosity weighted average),√s= 3.65 GeV and the ψ(3686) peak, respectively. Since the above energy points are close to τ+_τ−_{mass threshold, the production}

cross section does not follow a 1/s distribution. Thus, only a part of the e+_e−_→τ+_τ−_{background events is}

in-cluded in the off-resonance data samples. To correct for the full background from e+_e−_→τ+_τ−_{, we estimate the}

remaining contribution, Nuncanceled

τ+τ− , using the detection

efficiency from MC simulation and the cross section dif-ference at off-resonance energy points and the ψ(3686) peak, as well as the luminosity at the ψ(3686) peak. The estimated values are shown in Table 1.

The small numbers of surviving events from ψ_{(3686) → e}+_e−_{, µ}+_µ−_{, and τ}+_τ− _{in data do not need}

to be explicitly subtracted since these leptonic ψ(3686) decays have been included in the inclusive MC samples, and their effects are considered in the detection efficiency.

Table 1. Numbers of the observed hadronic events, Nobs

ψ(3686)(×106), numbers of the observed hadronic events in

off-resonance data, Nobs

off−resonance(×106), corresponding to the bottom plot in Fig. 5, numbers of the remaining e+e−→

τ+τ−_{events after subtracting the normalized off-resonance data, N}uncanceled

τ+_τ− (×10

6_{), the detection efficiencies, , of}

ψ(3686)→hadrons for different charged-track multiplicity requirements, and numbers of ψ(3686) events, Nψ(3686)

(×106).

multiplicity Ngood>1 Ngood>2 Ngood>3

year 2009 2012 2009 2012 2009 2012 Nobs ψ(3686) 107.72 343.51 103.72 329.04 82.28 259.98 N_{off−resonance}obs 2.23 1.325 2.01 1.245 0.74 0.400 Nuncanceled τ+_τ− 0.036 0.57 0.034 0.54 0.013 0.21 (%) 92.92 92.39 89.96 88.96 74.73 73.20 Nψ(3686) 107.2 341.7 107.2 340.5 106.6 343.6

θ

cos

Events/0.04

/E

E

Events/0.01

N

Events/1.0

N

Events/0.5

Fig. 7. (color online) Comparisons of data and MC simulation: (top-left) The cosθ distribution, (top-right)

Evisible/Ecm distribution, (bottom-left) charged-track multiplicity distribution, and (bottom-right) photon

mul-tiplicity distribution.

Table 1 also shows the numbers of the observed hadronic events for different charged-track multiplicity requirements of the ψ(3686) (Nobs

ψ(3686)) and off-resonance

data (Nobs

off−resonance). The corresponding detection

ef-ficiencies of ψ(3686) → hadrons are determined with 363.7×106 _{ψ(3686) inclusive MC events, and are also}

listed in this table. The branching fraction of ψ(3686)→ hadrons is included in the efficiency. Figure 7 shows the comparisons for cosθ, Evisible/Ecm, charged-track

multi-plicity, and photon multiplicity distributions after back-ground subtraction between data and MC simulation, and reasonable agreement between data and MC simu-lation is observed.

5

Numerical results

The number of ψ(3686) events, Nψ(3686), can be

cal-culated from

Nψ(3686)=

Nobs

peak−f·Noff−resonanceobs −Nτuncanceled+_τ−

 . (4)

With the numbers listed in Table 1, the numerical results for Nψ(3686) with different charged-track multiplicity

re-quirements are calculated and listed in Table 1. There are slight differences between different multiplicity re-quirements due to the imperfect MC simulation of the charged track multiplicity. To obtain a more exact

nu-merical result for Nψ(3686), an unfolding method is

em-ployed based on an efficiency matrix, whose matrix ele-ments, ij, represent the probability to observe i charged

tracks for an event with j actual charged tracks. The efficiency matrix is determined from the inclusive MC samples. In practice, there are even numbers of charged tracks generated in an event due to charge conservation, while any number of charged tracks can be observed due to the reconstruction efficiency and backgrounds. There-fore, the true charged track multiplicity of the data sam-ple is estimated from the observed multiplicity and the efficiency matrix by minimizing a χ2 _{value, defined as}

χ2₌ 10 X i=1  Nobs i − 10 P j=0 ij·Nj 2 Nobs i , (5)

where the values Ni

obs(i = 0, 1, 2,···) are the observed

multiplicities of charged tracks in data sample which correspond to the distribution in Fig. 7 (bottom-left, the points with error bars), while the values Nj (j =

0, 2, 4,···) are the true multiplicities of charged tracks in the data sample. They are the free parameters in the fit. For simplicity, the events with ten or more tracks are combined in a single value, N10. The value of Nψ(3686)

can be calculated by summing over all the obtained Nj.

and 2012 data samples, respectively.

6

Systematic uncertainties

The systematic uncertainties in the Nψ(3686)

mea-surement from different sources are described below and listed in Table 2. The total systematic uncertainty is de-termined by the quadratic sum of all individual values.

6.1 Polar angle

The polar angle acceptance for the charged tracks in the MDC is |cosθ| <0.93. From Fig. 7 (top-left), there is a slight difference between data and MC simulation at large polar angles. As a check, the requirement on the polar angle is changed to be |cosθ|<0.8. The differ-ence in Nψ(3686) is taken as the uncertainty due to the

requirement on the polar angle.

6.2 Tracking

A small difference (less than 1%) on the tracking ef-ficiency between data and MC simulation is observed by various studies [14]. Assuming the average efficiency dif-ference between data and MC simulation is 1% per track, the effect can be determined by randomly removing MC simulated tracks with a 1% probability. This results in a negligible difference in Nψ(3686), implying that Nψ(3686)

is not sensitive to the tracking efficiency. 6.3 Charged-track multiplicity

The effect due to the simulation of the charged-track multiplicity has been taken into account by the unfold-ing method described above. By comparunfold-ing the results between the direct calculation in Table 1 and the un-folding method including the Ngood61 events, there is

a difference of 0.2% on Nψ(3686) for both the 2009 and

2012 data, which is taken as the uncertainty associated with the charged-track multiplicity.

6.4 Momentum and opening angle

For the type-II events, the requirements on the mo-mentum of charged tracks and the opening angle between two charged tracks are applied to reject the sizable back-ground from Bhabha and dimuon events. When the re-quirement of charged track momentum is changed from P < 1.7 GeV/c to P < 1.55 GeV/c, the resultant change

in Nψ(3686) is negligible. When the requirement on

open-ing angle between two charged tracks is changed from θ < 176◦ _{to θ < 160}◦_{, the change in N}

ψ(3686) is

negligi-bly small for the 2009 data and is 0.04% for the 2012 data. Figure 8 shows comparisons of the distributions of the momentum and the opening angle of the two charged tracks after background subtraction in the type-II events between the data and inclusive MC simulation.

P (GeV/c)

Events/10 MeV/c

(degree)

∆

Events/0.2 degree

Fig. 8. (color online) Distributions of (top) charged

track momentum and (bottom) opening angle be-tween the two charged tracks for type-II events.

6.5 LEB contamination

Nψ(3686) is insensitive to the visible energy

require-ment. The uncertainty associated with the requirement

Evisble/Ecm> 0.4 is estimated by comparing the results

with or without this requirement, and the difference on

Nψ(3686) is assigned to be the corresponding uncertainty.

6.6 Determination of Nobs

As mentioned as in Sec. 3, two methods are used to obtain Nobs_{. The nominal method counts the numbers}

of events in the signal region and subtracts the number of background estimated in the sideband regions. The alternative method is performed by fitting the ¯VZ

distri-bution. The resultant difference on Nobs _{between these}

two methods is taken as the uncertainty in the determi-nation of Nobs_.

6.7 Vertex requirement

We repeat the analysis by changing the requirement Vr < 1 cm to Vr< 2 cm, and the change in Nψ(3686) is

small and is taken as the systematic uncertainty. Simi-larly, we repeat the analysis by changing the requirement | ¯VZ|<10cm to | ¯VZ|<20cm, and find a negligible change

6.8 Scaling factor

The scaling factor (f ) for the background subtrac-tion depends on the luminosity of the data samples. In the nominal analysis, the luminosity is estimated with e+_e−_{→ γγ events. An alternative measurement of the}

luminosity is performed with large angle Bhabha events, and the scaling factor as well as Nψ(3686)are recalculated.

The resultant difference in Nψ(3686) is found to be

negli-gible, and the corresponding uncertainty is negligible.

6.9 Choice of sideband region

In the nominal analysis, we take | ¯VZ|<4cm as the

sig-nal region and 6<| ¯VZ|<10cm as the sideband region. An

alternative analysis is done shifting the sideband region outward by 1 cm, which is about 1σ of the ¯VZ

resolu-tion. The resulting difference in Nψ(3686) is taken as the

systematic uncertainty.

6.10 π0 _{mass requirement}

The π0_{mass requirement is only applied for the}

type-I events. There is a slight change in Nψ(3686) when the

mass window requirement is changed from |Mγγ−Mπ0|<

0.015 GeV/c2 _{to |M}

γγ−Mπ0| < 0.025 GeV/c2. This

dif-ference is taken as the uncertainty due to the π0 _mass

requirement.

6.11 Missing Ngood=0 hadronic events

A detailed topological analysis is performed for the events with Ngood=0 in the inclusive MC sample. Most

of these events come from the well-known decay chan-nels, such as ψ(3686) → X + J/ψ (where X denotes η,π0_,π0_π0_{,γγ etc.) and ψ(3686) → e}+_e−_{, µ}+_µ−_{. The}

fraction of these Ngood= 0 events in the inclusive MC

sample is ∼2.0%, of which the pure neutral channels contribute about 1.0%. As shown in Fig. 7, the MC simulation models data well. Therefore, we investigate the pure neutral hadronic events, which are selected ac-cording to the following scheme. With the same charged track and shower selection criteria as above, we require Ngood= 0 and Nγ> 3. The latter requirement is used

to suppress e+_e−_{→γγ and beam-associated background}

events. The same selection criteria are imposed on the off-resonance data and inclusive MC events. Figure 9 shows the distributions of the total energies in the EMC, EEMC, for the different data sets and inclusive MC

sam-ple. The peaking events around the center-of-mass en-ergy are taken as the pure neutral hadronic candidates. As shown in Fig. 9, the number of signal events is deter-mined by a fit of the EEMC distribution. In this fit, the

signal is described by a Crystal Ball function, the QED background in ψ(3686) data is described by the shape of off-resonance data (off-resonance data at√s = 3.65 GeV or τ -scan data) after scaling for luminosity, and the other

backgrounds are described by a polynomial function. For the 2012 data, the difference in the number of pure neu-tral hadronic events between the data and the inclusive MC simulation sample is 11% if the τ -scan data sample is taken as the off-resonance data to estimate the back-ground function, as shown in Fig. 9 (top). However, this difference changes to 18% if we use the off-resonance data at√s=3.65GeV for the background function, as shown in Fig. 9 (middle). The larger difference is used to esti-mate the uncertainty conservatively. Since the fraction

(GeV) EMC E 2.6 2.8 3 3.2 3.4 3.6 3.8 4 Events/5 MeV 2000 4000 6000 8000 10000 (GeV) EMC E 2.6 2.8 3 3.2 3.4 3.6 3.8 4 Events/5 MeV 2000 4000 6000 8000 10000 (GeV) EMC E 2.6 2.8 3 3.2 3.4 3.6 3.8 4 Events/5 MeV 2000 4000 6000 8000 10000 12000 (GeV) EMC E 2.6 2.8 3 3.2 3.4 3.6 3.8 4 Events/5 MeV 2000 4000 6000 8000 10000 12000 (GeV) EMC E 2.6 2.8 3 3.2 3.4 3.6 3.8 4 Events/5 MeV 0 2000 4000 6000 8000 10000 (GeV) EMC E 2.6 2.8 3 3.2 3.4 3.6 3.8 4 Events/5 MeV 0 2000 4000 6000 8000 10000

Fig. 9. (color online) Distributions of the total

en-ergies in the EMC for the Ngood= 0 events for

(top) the ψ(3686) data with QED background ap-proximated by the τ -scan data, (middle) the data

taken at√s =3.65 GeV, and (bottom) the

inclu-sive ψ(3686) MC sample. The dot-dashed lines are the signal shapes of neutral ψ(3686) decays and the shaded regions are the background shapes from ψ(3686) decays. The dashed lines are the background shapes from QED processes.

Table 2. Systematic uncertainties (%).

source 2009 2012

polar angle 0.27 0.31

tracking negligible negligible

charged track multiplicity 0.20 0.19 momentum and opening angle negligible 0.04 LEB contamination negligible 0.09

Nobs_{determination 0.27 0.30}

vertex requirement 0.32 0.21

scaling factor (f ) negligible negligible choice of sideband region 0.32 0.26

π0_{mass requirement 0.09 0.05}

Ngood=0 events 0.25 0.18

MC modeling negligible negligible

trigger negligible negligible

B(ψ(3686)→hadrons) 0.13 0.13

total 0.70 0.63

of the pure neutral hadronic events is about 1.0% of the total selected candidates, the uncertainty due to the missing Ngood=0 events should be less than 18%×1%=

0.18% for the 2012 data. The same method is applied to the 2009 data samples, and the uncertainty is 0.25%, which is somewhat larger than the previous analysis [2].

6.12 MC modeling

The uncertainty due to the MC simulation of inclu-sive ψ(3686) decays arises from sources such as the input of branching fractions, the angular distributions of the known and unknown decay modes, etc. These uncertain-ties have been covered by those from the charged-track multiplicity, missing of Ngood= 0 events etc. Thus, no

further uncertainty is assigned for the MC modeling.

6.13 Trigger

Based on the 2009 data, the trigger efficiency for the Ngood>2 (type-II and type-III) events is close to 100.0%,

while it is 98.7% for the type-I events [15]. Since the frac-tion of type-I events is only about 3% of the total selected events, the uncertainty caused by the trigger is negligible for the 2009 data. As shown in Table 1, the fraction of type-I events in the 2012 data is the same as that in the 2009 data. Furthermore, an additional neutral trigger channel was added during 2012 data taking. Therefore, the trigger efficiency for the 2012 data is expected to be higher for type-I events than that for the 2009 data, and the uncertainty associated with the trigger is negligible.

6.14 B(ψ(3686)→hadrons)

The uncertainty of the branching fraction for ψ_{(3686) → hadrons is small, 0.13% [1] and taken as the} uncertainty.

7

Summary

The number of ψ(3686) events taken by BESIII in 2012 is measured to be (341.1±2.1)×106_{with the}

inclu-sive hadronic events, where the uncertainty is systematic and the statistical uncertainty is negligible. The num-ber of ψ(3686) events taken in 2009 is also updated to be (107.0±0.8)×106_{, which is consistent within the}

uncertainty with respect to the previous measurement, and the improved precision is due to the refined offline software, MC tuning, and the improved method to de-termine Nψ(3686). Adding the results linearly yields the

total number of ψ(3686) events for the two runs to be (448.1±2.9)×106_{. This work provides an important}

pa-rameter for the studies of the decays of the ψ(3686) and its daughters.

The BESIII collaboration thanks the staff of BEPCII and the computing center for their hard efforts.

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